(Bloomberg) -- When Grace Anderson prints out her resume, she notices 20 percent of it is missing. Still, her qualifications are so good that she’s offered the job she seeks by a man who says, "We think you’ll be pleased with the offer -- that we gave someone else. You’ll be making 20 percent less."

Grace is a character in a video prepared for Equal Pay Day on April 4 by LeanIn.org, the women’s empowerment group founded by Facebook Inc. Chief Operating Officer Sheryl Sandberg. While the humorous video shows blatant discrimination, the reality of the gender wage gap is far more complex and opaque.

Though many companies, including Facebook, say they pay men and women equally, they are loath to share the data, even when pressed by investors, employees and government regulators.

The most prominent recent example is Alphabet Inc.’s Google. A Department of Labor official said in court on Friday that it has found "systemic compensation disparities" against women at the company. In a statement late Monday, Google said it was "taken aback by this assertion, which came without any supporting data or methodology."

The DOL sued the company in January for refusing to provide compensation information as part of a compliance audit of federal contractors. The agency declined to comment, citing the ongoing case.

"Very few companies have opened the black box," said Emily Martin, vice president for workplace justice at the National Women’s Law Center. "Most have just said, ‘trust us.’"

Without transparency on how compensation gap statistics are calculated, including pay and job categories used, "it’s hard to know if their analysis is credible," she added.

Calculating a gender pay gap requires a significant amount of data, said Linda Chen, a principal at Mercer, the consulting firm that performs the analyses for many companies. That could include hire date, education, role, overtime, bonus, and even performance ratings, usually taken as a snapshot at a particular point in time. Most companies store this in their human resources information systems, she said.

The DOL asked Google for a snapshot of its workforce as of Sept. 1, 2015, and Sept. 1, 2014, according to the lawsuit, which seeks to bar the company from federal contracts if it doesn’t comply. Google currently gets only a few million dollars annually in federal contracts, according to Bloomberg BNA. That’s a pittance compared to its $90 billion revenue last year, but the company has big aspirations for its cloud-computing business and losing the U.S. government as a potential customer would be a blow.

In a blog post on Monday, Eileen Naughton, Google’s human resources chief, wrote that the company sets compensation each year using analysts who don’t know the gender of employees. If women or men, as a group, are paid a statistically significantly lower amount, Google adjusts to bring the group’s pay in line, she said.

Still, Google should give the government the data it’s seeking so that it can explain the gaps the DOL is signaling, said Martin of the National Women’s Law Center. "The things they say they’re doing sound like the right kind of things," she added. Not sharing its information "makes it look like they have something to hide."

Increased regulatory and public scrutiny of pay means that "we have seen a surge in the past couple of years in companies that are looking at it pro-actively," said Mercer’s Chen.

While working women overall make about 20 percent less than men, the gap shrinks to about 5.6 percent when controlled for specific job roles, seniority, and other factors according to Glassdoor Inc., operator of a job and career site. At tech companies, the gap is about 5.9 percent.

Many tech companies, prodded by shareholders, last year announced they had studied the amounts they pay men and women and that there either was no gap or that it was small and they were taking steps to close it. Google blocked an investor request to report on any gender pay gaps at its annual meeting last year. A former Google software engineer, Erica Baker, said in 2015 that she was reprimanded by her manager after she created a spreadsheet on the company’s internal social network where workers could share compensation information.

Glassdoor on Tuesday said its salary data showed male Google employees earn about 16.3 percent more than women, but that an apples-to-apples comparison adjusted for similar jobs and backgrounds shrinks the gap to about 1.6 percent. That’s "not statistically significant from zero," Glassdoor chief economist Andrew Chamberlain said in a blog post.

But even a 1 percent pay gap companywide can be statistically significant, especially if the gap is persistent over time, said Chen, who was speaking generally and not about Google in particular.

Pay audits often reveal broader issues in the workplace, such as the lack of women in a particular job category. "Pay equity is a great tip-of-the-spear analysis, because it can open up a broader range of areas that need to be addressed," she said. "Maybe we can explain away the entire pay gap, but that doesn’t mean the work is done."

For instance, women make up just 18 percent of all software developers, according to the Institute for Women’s Policy Research. In that category, they earn 20 percent less than men. At Google, women hold 19 percent of technical jobs, according to the company’s web site.

Some shareholders want companies to pay workers fairly, and have stepped up pressure. In the 2017 proxy season, investors have filed at least 18 pay equity proposals, according to ISS Corporate Solutions. That compares with 13 in 2016 and just one in 2015, the first year ISS recorded such actions.

Both Facebook and Google are facing -- and opposing -- shareholder proposals on gender pay equity for the second year in a row. With insiders controlling voting rights through special classes of stock, the proposals won’t pass, but they draw further attention to the issue.

Last year, almost half of the non-insider investors voted in favor of the proposal at Google, according to Natasha Lamb, director of shareholder engagement at Arjuna Capital, which filed the proposal with Proxy Impact and The Sustainability Group. But that translated into just 12 percent of voting rights because of the special shares owned by management. The proposal sought a gender pay gap measurement that included base salary, bonus and equity awards if possible, and a commitment to close any gap that was found.

Proxy Impact Chief Executive Officer Michael Passoff said he held his first call with Google in March 2016 asking for more disclosure on pay structures. At the time, Google promised a fuller report by October of that year, but it didn’t come, Passoff said. "This year, they have been completely non-responsive," he added.

At Facebook, too, the Arjuna proposal failed. It will go to a vote again at the company’s annual meeting this year. "Facebook falls in the laggard category along with Google in actually disclosing their pay gap number," Lamb said. Sandberg "has been nothing short of a hypocrite on gender pay equity -- no numbers, no accountability, no authentic leadership."

Lori Matloff Goler, Facebook’s global head of human resources, said the company built systems many years ago to ensure that men and women are paid equally. She said last year that the company had no gender wage gap, and reiterated that last week.